Question

A Ladder makes an angle of ${60}^{\circ }$ with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length( in meters) is:

• A.
• B.
• C.
• D. 4

Answer 1

The correct option is D

4

In the figure, MN is the length of the ladder, which is placed against the wall AB and makes an angle of ${60}^{\circ }$ with the ground.
The foot of the ladder is at N, which is 2m away from the wall.
$\therefore BN=2m$
In right-angled triangle MNB :
$cos{60}^{\circ }=\frac{BN}{MN}=\frac{2m}{MN}$
$\Rightarrow \frac{1}{2}=\frac{2m}{MN}$
$\Rightarrow MN=4m$
Therefore, the length of the ladder is 4m.
Hence, the correct option is D